I set two sets of keyframes with the same parameters but I still get movement in between them. I looked at the interpolation graph and there's always a hump in between them. No matter how much I fiddle I can never get something to stay still for a moment.

It's not absolutely necessary to do this in the Graph Editor. If you want to ease into a static position and ease out again, you can highlight the incoming keyframe, ritht-click on it, and select the Toggle Hold Keyframe command. You'll get rid of the annoying motion in the middle.

This ping pong movement is also visible in the comp window when you look at the keyframes. You can simply select the pen tool using the G key and then Alt/Option click the offending keyframe to fix the problem. This only effects the keyframe selected where changing all keyframe interpolation to linear changes the timing of the entire animation.